Current mode control utilizing plant inversion decoupling in electric power steering systems

ABSTRACT

A system includes a first module that: receives the output current from the electric motor as a feedback, the output current including a direct axis component and a quadrature axis component; and generates a first voltage command based on a virtual resistance value, the feedback, and a targeted frequency characteristic of the motor control system. The system includes: a second module that: receives a difference between the feedback and a commanded current; and generates a second voltage command based on an estimated inductance value, an estimated resistance value of an electric motor, the virtual resistance value, a targeted frequency response characteristic of the motor control system, and the response of the d-axis component of the output current being decoupled from the response of the q-axis component. The system includes an addition module that generates an input voltage command for the electric motor by adding the first and second voltage commands.

BACKGROUND

The present application is generally related current mode controlutilizing plant inversion decoupling in electric power steering (EPS)systems.

The output torque of a PMSM (either a surface permanent magnet (SPM) oran interior permanent magnet (IPM) motor) may be determined by a voltagecommand and a phase advance angle. A specific output torque of the PMSMis determined by first selecting a specific quadrature axis (alsoreferred to as the q-axis) reference current and a direct axis (alsoreferred to as the d-axis) reference current, and then determining thevoltage command and the phase advance angle based on the selectedquadrature axis reference current and the direct axis reference current.

EPS systems use an electric motor (e.g., PMSM) to provide steeringassist. When using a PMSM, Field Oriented Control (FOC) is utilized,which allows an alternating current (AC) poly-phase (e.g., three-phase)motor voltage and current signals to be transformed into a synchronouslyrotating reference frame, commonly referred to as the d-axis/q-axisreference frame, where the motor voltages and currents become directcurrent (DC) quantities. The FOC torque control technique is implementedeither using feedforward methods of control or a closed-loop currentfeedback control, or some combination of them.

Application of closed-loop current control of PMSM to EPS systems hasunique and demanding requirements outside of the control system'scapability to track the desired assist torque command (i.e., motortorque command) Many of these requirements are associated with a balanceof the torque response behavior, motor input disturbancecharacteristics, current measurement noise transmission characteristics,and robustness to the accuracy of the estimated electric motor parameterestimates. Consistency of performance throughout the operating range ofthe control system is desired, including operation throughout the motorvelocity range and operation near the supply voltage limit. Unlike highvoltage power applications utilizing PMSMs, the supply voltage availablefor the control system from a vehicle is limited, and the motor used inthese applications is typically sized as efficiently as possible todeliver steady state power requirements. This requires the currentcontrol to operate in a stable and predictable manner as the transientvoltage available to the control system becomes smaller near the peakpower point of PMSM operation. Therefore, the control system should beconfigured to operate as desired while requiring relatively small motorvoltage command transients.

SUMMARY

According to one or more embodiments, motor control system thatgenerates an output current from an input voltage includes a firstmodule, a second module, and an addition module. The first module isconfigured to: receive the output current from the electric motor as afeedback, the output current including a direct axis (d-axis) componentand a quadrature axis (q-axis) component; and generate a first voltagecommand based on a virtual resistance value, the feedback, and atargeted frequency characteristic of the motor control system. Thesecond module is configured to: receive a difference between thefeedback and a commanded current; and generate a second voltage commandbased on an estimated inductance value, an estimated resistance value ofan electric motor, the virtual resistance value, a targeted frequencyresponse characteristic of the motor control system, and the response ofthe d-axis component of the output current being decoupled from theresponse of the q-axis component, the motor control system being aclosed-loop system. The addition module is configured to generate aninput voltage command for the electric motor by adding the first voltagecommand and the second voltage command.

According to one or more embodiments, a steering system includes anelectric motor and a motor control system. The motor control systemincludes a first module, a second module, and an addition module. Thefirst module is configured to: receive the output current from theelectric motor as a feedback, the output current including a direct axis(d-axis) component and a quadrature axis (q-axis) component; andgenerate a first voltage command based on a virtual resistance value,the feedback, and a targeted frequency characteristic of the motorcontrol system. The second module is configured to: receive a differencebetween the feedback and a commanded current; and generate a secondvoltage command based on an estimated inductance value, an estimatedresistance value of an electric motor, the virtual resistance value, atargeted frequency response characteristic of the motor control system,and the response of the d-axis component of the output current beingdecoupled from the response of the q-axis component, the motor controlsystem being a closed-loop system. The addition module is configured togenerate an input voltage command for the electric motor by adding thefirst voltage command and the second voltage command.

According to one or more embodiments, a method includes method thatgenerates an output current from an input voltage includes receiving, bya first module, the output current from the electric motor as afeedback, the output current including a direct axis (d-axis) componentand a quadrature axis (q-axis) component. The method further includesgenerating, by the first module, a first voltage command based on avirtual resistance value, the feedback, and a targeted frequencycharacteristic of the motor control system. The method further includesreceiving, by the second module, a difference between the feedback and acommanded current. The method further includes generating, by the secondmodule, a second voltage command based on an estimated inductance value,an estimated resistance value of an electric motor, the virtualresistance value, a targeted frequency response characteristic of themotor control system, and the response of the d-axis component of theoutput current being decoupled from the response of the q-axiscomponent, the motor control system being a closed-loop system. Themethod further includes generating, by an addition module, an inputvoltage command for the electric motor by adding the first voltagecommand and the second voltage command.

These and other advantages and features will become more apparent fromthe following description taken in conjunction with the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The subject matter of the present disclosure is particularly pointed outand distinctly claimed in the claims at the conclusion of thespecification. The foregoing and other features, and advantages of thepresent disclosure are apparent from the following detailed descriptiontaken in conjunction with the accompanying drawings in which:

FIG. 1A is an embodiment of an electric power steering system suitablefor implementation of the disclosed embodiments;

FIG. 1B is an exemplary schematic illustration of a motor control systemin accordance with exemplary embodiments;

FIGS. 2A and 2B depict control system topologies according to one ormore embodiments of the present invention;

FIG. 3 depicts the control system topology FIG. 2B in more detailaccording to one or more embodiments of the present invention;

FIG. 4 depicts a block diagram of a motor (plant model) according to oneor more embodiments of the present invention;

FIG. 5 depicts a block diagram of IIDC architecture according to one ormore embodiments of the present invention;

FIG. 6 depicts a block diagram of an IIDC architecture for second orhigher order transfer function response according to one or moreembodiments of the present invention; and

FIG. 7 depicts a block diagram of an IIDC architecture for transferfunction response of different orders in both the q-axis loop and thed-axis loop according to one or more embodiments of the presentinvention.

DETAILED DESCRIPTION

Referring now to the figures, where the present disclosure will bedescribed with reference to specific embodiments, without limiting thesame, it is to be understood that the disclosed embodiments are merelyillustrative of the present disclosure that may be embodied in variousand alternative forms. The figures are not necessarily to scale; somefeatures may be exaggerated or minimized to show details of particularcomponents. Therefore, specific structural and functional detailsdisclosed herein are not to be interpreted as limiting, but merely as arepresentative basis for teaching one skilled in the art to variouslyemploy the present disclosure.

As used herein the terms module and sub-module refer to one or moreprocessing circuits such as an application specific integrated circuit(ASIC), an electronic circuit, a processor (shared, dedicated, or group)and memory that executes one or more software or firmware programs, acombinational logic circuit, and/or other suitable components thatprovide the described functionality. As can be appreciated, thesub-modules described below can be combined and/or further partitioned.

Referring now to the figures, where the technical solutions will bedescribed with reference to specific embodiments, without limiting same,FIG. 1A is an embodiment of an electric power steering system (EPS) 40suitable for implementation of the disclosed embodiments. The steeringmechanism 36 is a rack-and-pinion type system and includes a toothedrack (not shown) within housing 50 and a pinion gear (also not shown)located under gear housing 52. As the operator input, hereinafterdenoted as a steering wheel 26 (e.g., a hand wheel and the like), isturned, the upper steering shaft 29 turns and the lower steering shaft51, connected to the upper steering shaft 29 through universal joint 34,turns the pinion gear. Rotation of the pinion gear moves the rack, whichmoves tie rods 38 (only one shown) in turn moving the steering knuckles39 (only one shown), which turn a steerable wheel(s) 44 (only oneshown).

Electric power steering assist is provided through the control apparatusgenerally designated by reference numeral 24 and includes the controller16 and an electric machine 19, which could be a permanent magnetsynchronous motor (PMSM), and is hereinafter denoted as motor 19. Thecontroller 16 is powered by the vehicle power supply 10 through line 12.The controller 16 receives a vehicle speed signal 14 representative ofthe vehicle velocity from a vehicle velocity sensor 17. Steering angleis measured through position sensor 32, which may be an optical encodingtype sensor, variable resistance type sensor, or any other suitable typeof position sensor, and supplies to the controller 16 a position signal20. Motor velocity may be measured with a tachometer, or any otherdevice, and transmitted to controller 16 as a motor velocity signal 21.A motor velocity denoted ω_(m) may be measured, calculated or acombination thereof. For example, the motor velocity ω_(m) may becalculated as the change of the motor position θ as measured by aposition sensor 32 over a prescribed time interval. For example, motorspeed ω_(m) may be determined as the derivative of the motor position θfrom the equation ω_(m)=Δθ/Δt where Δt is the sampling time and Δ0 isthe change in position during the sampling interval. Alternatively,motor velocity may be derived from motor position as the rate of changeof position with respect to time. It will be appreciated that there arenumerous well-known methodologies for performing the function of aderivative.

As the steering wheel 26 is turned, torque sensor 28 senses the torqueapplied to the steering wheel 26 by the vehicle operator. The torquesensor 28 may include a torsion bar (not shown) and a variableresistive-type sensor (also not shown), which outputs a variable torquesignal 18 to controller 16 in relation to the amount of twist on thetorsion bar. Although this is one type of torque sensor, any othersuitable torque-sensing device used with known signal processingtechniques will suffice. In response to the various inputs, thecontroller sends a command 22 to the electric motor 19, which suppliestorque assist to the steering system through worm 47 and worm gear 48,providing torque assist to the vehicle steering.

It should be noted that although the disclosed embodiments are describedby way of reference to motor control for electric steering applications,it will be appreciated that such references are illustrative only andthe disclosed embodiments may be applied to any motor controlapplication employing an electric motor, e.g., steering, valve control,and the like. Moreover, the references and descriptions herein may applyto many forms of parameter sensors, including, but not limited totorque, position, speed and the like. It should also be noted thatreference herein to electric machines including, but not limited to,motors, hereafter, for brevity and simplicity, reference will be made tomotors only without limitation.

In the control system 24 as depicted, the controller 16 utilizes thetorque, position, and speed, and like, to compute a command(s) todeliver the required output power. Controller 16 is disposed incommunication with the various systems and sensors of the motor controlsystem. Controller 16 receives signals from each of the system sensors,quantifies the received information, and provides an output commandsignal(s) in response thereto, in this instance, for example, to themotor 19. Controller 16 is configured to develop the correspondingvoltage(s) out of inverter (not shown), which may optionally beincorporated with controller 16 and will be referred to herein ascontroller 16, such that, when applied to the motor 19, the desiredtorque or position is generated. In one or more examples, the controller24 operates in a feedback control mode, as a current regulator, togenerate the command 22. Alternatively, in one or more examples, thecontroller 24 operates in a feedforward control mode to generate thecommand 22. Because these voltages are related to the position and speedof the motor 19 and the desired torque, the position and/or speed of therotor and the torque applied by an operator are determined. A positionencoder is connected to the steering shaft 51 to detect the angularposition θ. The encoder may sense the rotary position based on opticaldetection, magnetic field variations, or other methodologies. Typicalposition sensors include potentiometers, resolvers, synchros, encoders,and the like, as well as combinations comprising at least one of theforegoing. The position encoder outputs a position signal 20 indicatingthe angular position of the steering shaft 51 and thereby, that of themotor 19.

Desired torque may be determined by one or more torque sensors 28transmitting torque signals 18 indicative of an applied torque. One ormore exemplary embodiments include such a torque sensor 28 and thetorque signal(s) 18 therefrom, as may be responsive to a complianttorsion bar, T-bar, spring, or similar apparatus (not shown) configuredto provide a response indicative of the torque applied.

In one or more examples, a temperature sensor(s) 23 located at theelectric machine 19. Preferably, the temperature sensor 23 is configuredto directly measure the temperature of the sensing portion of the motor19. The temperature sensor 23 transmits a temperature signal 25 to thecontroller 16 to facilitate the processing prescribed herein andcompensation. Typical temperature sensors include thermocouples,thermistors, thermostats, and the like, as well as combinationscomprising at least one of the foregoing sensors, which whenappropriately placed provide a calibratable signal proportional to theparticular temperature.

The position signal 20, velocity signal 21, and a torque signal(s) 18among others, are applied to the controller 16. The controller 16processes all input signals to generate values corresponding to each ofthe signals resulting in a rotor position value, a motor speed value,and a torque value being available for the processing in the algorithmsas prescribed herein. Measurement signals, such as the above mentionedare also commonly linearized, compensated, and filtered as desired toenhance the characteristics or eliminate undesirable characteristics ofthe acquired signal. For example, the signals may be linearized toimprove processing speed, or to address a large dynamic range of thesignal. In addition, frequency or time-based compensation and filteringmay be employed to eliminate noise or avoid undesirable spectralcharacteristics.

In order to perform the prescribed functions and desired processing, aswell as the computations therefor (e.g., the identification of motorparameters, control algorithm(s), and the like), controller 16 mayinclude, but not be limited to, a processor(s), computer(s), DSP(s),memory, storage, register(s), timing, interrupt(s), communicationinterface(s), and input/output signal interfaces, and the like, as wellas combinations comprising at least one of the foregoing. For example,controller 16 may include input signal processing and filtering toenable accurate sampling and conversion or acquisitions of such signalsfrom communications interfaces. Additional features of controller 16 andcertain processes therein are thoroughly discussed at a later pointherein.

FIG. 1B illustrates a motor control system 100 in accordance with oneaspect of the invention. In the exemplary embodiments as shown, themotor control system 100 includes a motor 19, an inverter 122, a supplyvoltage 124, and a control module 130 (also referred to as acontroller). The voltage supply 124 supplies a supply voltage V_(B) tothe motor 19. In some embodiments, the voltage supply 124 is a battery.However, it is to be understood that other types of voltage supplies maybe used as well. The inverter 122 is connected to the motor 19 by aplurality of connections 132 (e.g., three connectors). In someembodiments, the motor 19 is a poly-phase permanent magnet synchronousmotor (PMSM). In this example, the motor 19 is a three-phase PMSM. Thecontrol module 130 is connected to the motor 19 through the inverter122. The control module 130 receives a motor torque command T*, whichmay be the output of another system such as, for example, the electricpower steering system (EPS) 40. The control module 130 includes controllogic for sending a motor voltage V to the motor 19 through the inverter122. Referring now to FIG. 1B, the motor 19 is operated such that aphase of the motor voltage command V shifts with respect to a phase of adeveloped back electromotive force (BEMF) voltage E of the motor 19. Insome embodiments, an encoder (not shown) is used to measure an angularposition θ of a rotor (i.e., mechanical position of the rotor) of themotor 19. The angular position θ of the motor 19 is converted to theelectrical position θ_(e) and is then used to determine the input phasevoltages. The motor 19 rotates in a clockwise as well as acounterclockwise direction and produces torque in both the clockwise andcounterclockwise direction during operation.

Permanent magnet synchronous machines (PMSMs), such as the motor 19 ofFIGS. 1A and 1B, are ubiquitous for electric drive applications due totheir advantages such as high power density, easy controllability, andimproved reliability. One commonly implemented control technique forPMSMs is vector control, in which all AC signals are transformed into DCsignals via a reference frame transformation. The control system is thenimplemented in the synchronously rotating or d/q reference frame.

According to one or more embodiments of the present invention, atechnique referred to as plant inversion decoupling current control(PIDCC) is provided to improve the robustness of an EPS system todisturbances, parameter inaccuracies, and imperfect decoupling. PIDCCuses a forward path controller C(s) to perform decoupling of the d and qaxes control loops while a feedback compensator H is implement toimprove plant dynamics. The specific utilization of two controllers(i.e., the forward path controller and the feedback compensator) resultsin an overall system that possesses the desirable properties mentionedabove.

In one embodiment, the forward path controller C(s) is split intoparallel controllers including a proportional controller C_(P) and anintegral controller G. After C(s) is split, the compensators C_(P) andC_(i) are not functions of “s.” The integration module 1/s is the onlyblock of the split C(s) that contains “s.” For this embodiment, thedecoupling is performed by the integral controller C_(I), and a firstorder closed loop response with a selectable cutoff frequency in bothcontrol loops is achieved. Higher order transfer functions for eitherloop can also be achieved by utilizing a different structure for theforward path controller C(s). The elements of the forward pathcontroller C(s) for PIDCC technique may be functions of the motorvelocity, machine parameters, and the desired closed loop cutofffrequencies, in which case the calibration and tuning of the controlsystem becomes greatly simplified, while delivering consistent torquecontrol response throughout the entire operating range of the electricmotor. Additionally, this provides for control system configuration tobalance multiple challenging design goals.

FIGS. 2A and 2B depict control system topologies 200, 201. FIG. 2Adepicts the forward path controller C(s) 202 as a single controller,while FIG. 2B depicts the proportional controller C_(P) 212 and theintegral controller C_(I) 214 as parallel controllers in place of theforward path controller C(s) 202.

A current reference vector I_(R), defined as a 2×1 vector consisting ofa d-axis and a q-axis component, is combined with a feedback signal 210,which represents a measured motor current vector I_(M). The combinedsignal I_(E) is fed into the forward path controller C(s) 202 (in FIG.2A) or the proportional controller C_(P)(s) 212 and the integralcontroller C_(I)(s) 214 (in FIG. 2B) to generate a voltage command. InFIG. 2A, the voltage command is a voltage command V_(C) from the forwardpath controller C(s) while in FIG. 2B, the voltage command V_(C) is acombination of a proportional voltage command V_(P) and an integralvoltage command V_(I) generated from the proportional controller C_(P)212 and the integral controller C_(I) 214 respectively. It should beappreciated that an integration module 216 can be utilized inconjunction with the integral controller C_(I) 214 to integrate thecombined signal I_(E). It is to be noted that each of I_(R), I_(M),I_(E), V_(P), V_(I), and V_(C) has a d-axis component and a q-axiscomponent. Also, I_(R), I_(M), I_(E), V_(P), V_(I), and V_(C) representvectors and not scalar values.

The voltage command V_(C) is combined with a voltage V_(F) from afeedforward back electromotive force (BEMF) compensation matrix 204. Thefeedforward BEMF compensation matrix 204 is used to compensate for slow(compared to current loop dynamics) dynamics of motor back electromotiveforce voltage. The voltage command V_(C) is also combined with a voltagecommand V_(H) from a feedback compensator H(s) 206. Together, thecombination of the voltage command V_(C), the voltage V_(F), and thevoltage command V_(H) are designated as voltage command vector V_(R),which is also defined as a 2×1 vector consisting of a d-axis and aq-axis component. The voltage command vector V_(R) gets combined with anexternal disturbance voltage V_(dist), having a d-axis component and aq-axis component, to generate a voltage V_(M), which is fed into a planttransfer matrix P(s) 208. The “V” terms have a “V_(d)” and a “V_(q)”component, not “I_(d)” and “I_(q).” V_(F) would be split into V_(Fd) andV_(Fq) whereas I_(M) would be split into I_(Md) and I_(Mq) and so on.Note that unlike C_(P) and C_(i), the plant transfer matrix P(s) doesnot contain “s” terms.

The plant transfer matrix P(s) 208 outputs a developed motor currentvector I_(P), which gets combined with an external disturbance currentI_(dist) (having a d-axis component and a q-axis component) to generatea current I_(A). The current I_(A) gets combined with an I_(noise)external disturbance current (also having a d-axis component and aq-axis component) to generate the measured motor current vector I_(M).The measured motor current vector I_(M) can be fed into the feedbackcompensator H 206 and as the feedback signal 210.

FIG. 3 depicts the control system topology 201 of FIG. 2B in more detailaccording to one or more embodiments of the present invention. It shouldbe appreciated that the plant matrix P(s) 208 is shown as an inverse todepict how the elements of the feedback compensator H 206 affect the“effective plant” dynamics.

Traditional approaches to current mode control have utilized directinversion decoupling control or enhanced feedback decoupling control.Direct inversion decoupling control utilizes C_(I) to decouple theplant, and does not use H. Enhanced feedback decoupling control utilizesH to decouple the plant and enhance plant dynamics while using C(s) toobtain desired closed loop transfer function order for the two controlloops. In contrast to these traditional approaches, the presenttechniques use plant inversion decoupling for current mode control.

The following equations defined in the d/q axis coordinate framedescribe the plant transfer function (using line to neutraldefinitions):

$V_{d} = {{L_{d}\frac{{dI}_{d}}{dt}} + {RI}_{d} + {\frac{N_{p}}{2}\omega_{m}L_{q}I_{q}}}$$V_{q} = {{L_{q}\frac{{dI}_{q}}{dt}} + {RI}_{q} - {\frac{N_{p}}{2}\omega_{m}L_{d}I_{d}} + {K_{e}\omega_{m}}}$$T_{e} = {{\frac{3}{2}K_{e}I_{q}} + {\frac{3}{4}{N_{p}\left( {L_{q} - L_{d}} \right)}I_{d}I_{q}}}$

where V_(d), V_(q) are the d/q motor voltages (in Volts); I_(d), I_(q)are the d/q motor currents (in Amperes); L_(d), L_(q) are the d/q axismotor inductances (in Henries); R is the motor circuit (motor pluscontroller) resistance (in Ohms); K_(e) is the motor BEMF coefficient(in Volts/rad/s); ω_(m) is the mechanical motor velocity (in rad/s); andT_(e) is the electromagnetic motor torque (in Nm). It should beappreciated that the torque equation is nonlinear and represent a sum ofthe torque developed by leveraging the magnetic field from the permanentmagnets, and the reluctance torque generated by rotor saliency(difference between L_(q) and L_(d)) and proper choice of I_(q) andI_(d).

Motor parameters vary significantly during normal operation, potentiallyover 100% variation in R, 5-20% variation in inductances L_(d), L_(q),and 15-20% variation in K_(e). R varies with build and temperature,L_(d), L_(q) vary due to saturation (i.e., as a function of I_(d),I_(q)), and K_(e) varies due to saturation (as a function of I_(q)) andwith temperature. Accordingly, the above equations can be rewritten asfollows:

V _(d) =L _(d) İ _(d) +RI _(d)+ω_(e) L _(q) I _(q)

V′ _(q) =V _(q) −K _(e)ω_(m) =L _(q) İ _(q) +RI _(q)−ω_(e) L _(q) I _(q)

In these rewritten equations,

$\omega_{e} = {\frac{N_{P}}{2}\omega_{m}}$

is the electrical speed of the machine. In order to employ standardlinear feedback control design techniques, the machine speed is assumedto be a slowly varying parameter. In addition, due to relatively slowflux dynamics, the quasi-static BEMF term K_(e) ω_(m) can be consideredto be essentially constant, which is compensated as a disturbance in thefeedforward path. These two assumptions allow linearization of these twoequations for a fixed speed. Note that the apostrophe in the V′_(q) termis dropped hereafter.

The two previous equations can be compactly rewritten using s-domainrepresentation as follows:

$U = {{{P_{i}(s)}{X\begin{bmatrix}V_{d} \\V_{q}\end{bmatrix}}} = {\begin{bmatrix}{{L_{d}s} + R} & {\omega_{e}L_{q}} \\{{- \omega_{e}}L_{d}} & {{L_{q}s} + R}\end{bmatrix}\begin{bmatrix}I_{d} \\I_{q}\end{bmatrix}}}$

Note that this description translates plant outputs into inputs via thecomplex frequency transfer matrix P_(i)(s) and is therefore the inverseof the true plant transfer matrix (i.e., the plant matrix P(s) 208) asshown in detail at block 208 of FIG. 3. The actual plant transfer matrixP(s), which converts plant inputs to outputs and is equal to the inverseof P_(i)(s) can be written as follows:

$\mspace{79mu} {X = {{{P(s)}{U\begin{bmatrix}I_{d} \\I_{q}\end{bmatrix}}} = {{{\frac{1}{{L_{d}L_{q}s^{2}} + {{R\left( {L_{d} + L_{q}} \right)}s} + R^{2} + {\omega_{e}^{2}L_{d}L_{q}}}\begin{bmatrix}{{L_{q}s} + R} & {{- \omega_{e}}L_{q}} \\{\omega_{e}L_{d}} & {{L_{d}s} + R}\end{bmatrix}}\begin{bmatrix}V_{d} \\V_{q}\end{bmatrix}} = {{\frac{1}{\Delta (s)}\begin{bmatrix}{{L_{q}s} + R} & {{- \omega_{e}}L_{q}} \\{\omega_{e}L_{d}} & {{L_{d}s} + R}\end{bmatrix}}\begin{bmatrix}V_{d} \\V_{q}\end{bmatrix}}}}}$

Note that the V_(q) in the equation above is actuallyV′_(q)=V_(q)−K_(e)ω_(m). Accordingly, the block diagram of the plant 400is shown in FIG. 4. This embodiment employs the transfer matrixdescription of the system because, in addition to achieving decoupling,it enables for employing classical techniques to analyze both loopsindividually. Although not shown in any of the figures, the controlsystem 200 may include a time delay component between the voltage outputof the controller V_(R) and the actual voltage input to the motor V_(M).

The system output response in terms of the reference inputs anddisturbances, which is the closed loop transfer matrix of the system,can be obtained as follows:

I _(A) =BP _(e) CI _(R) +BP _(e) V _(dist) +BP _(e) P ⁻¹ I _(dist) +BP_(e)(H−C)I _(noise)

B=(I+P _(e) C)⁻¹

I _(A) =TI _(R) +T _(Di) V _(dist) +T _(Do) I _(dist) +T _(Dn) I_(noise)

As shown, these equations are written in terms of the effective plantmatrix, which is defined as P_(e)=(P⁻¹−H)⁻¹. It should be appreciatedthat the effective plant can be defined as the effective transfer matrixfrom V_(c) to I_(m) if no disturbances are present. In other words, theeffective plant P_(e) is the resultant plant as observed by the forwardpath controller C(s) 202.

It should be appreciated that the transfer matrices involving systemresponses to various disturbances are not directly utilized fordesigning the control system. However, these transfer matrices arehelpful in performing robustness and sensitivity analysis of thedifferent control system configurations to disturbances. Thus, thefollowing derivations are performed with disturbances nullified, and thesystem output can be written as follows:

I _(A) =I _(M)=(I+P _(e) C)⁻¹ P _(e) CI _(R)

The open loop transfer matrix L, which relates to the tracking errorI_(E) to the system outputs I_(A)=I_(M) can be obtained as follows:

I _(A) =P _(e) CI _(E) =LI _(E)

Further, the voltage command in the absence of disturbances isV_(r)=V_(m). It should be appreciated that the closed loop and open looptransfer matrices are related as T=(I+L)⁻¹L. The open loop transfermatrix can therefore be written as follows:

L=P _(e) C

With reference to FIGS. 2A, 2B, and 3, plant inversion decouplingcurrent control design utilizes the output forward path integralcontroller C_(I) 214 to decouple the plant, and the feedback compensatorH 206 to enhance plant dynamics. There are two aspects to plantinversion decoupling. First, the off-diagonal elements of the integralcontroller C_(I) 214 are configured to cancel the coupling terms in theplant equations. This allows for changes in V_(q) to control I_(q)without affecting I_(d) and changes in V_(d) to control I_(d) withoutaffecting I_(q).

Second, the diagonal elements of the integral controller C_(I) 214 areconfigured to modify virtual resistance to the plant so that the“effective resistance” of the plant increases. The virtual resistanceaids in removing the undesirable characters of direct inverse decouplingincluding resonances near the operating speed of the plant, sensitivityto changes in the motor circuit resistance (i.e., parameter estimationaccuracy issues with the motor circuit resistance estimate) as well asother parameter estimates, and improving robustness to plant inputdisturbances as well as imperfect decoupling. Configuration of thevalues of these elements is performed carefully to achieve a balancedtradeoff between desired plant input disturbance transfer functioncharacteristics and noise transmissibility (I_(noise) to I_(A) transfermatrix) characteristics.

In order to utilize plant inversion decoupling current control (PIDDC),it is important to derive the open loop transfer matrix in terms of thecontroller matrix gains, which may be done as follows:

$\mspace{79mu} \begin{matrix}{P_{e} = \left( {\begin{bmatrix}{{L_{d}s} + R} & {\omega_{e}L_{q}} \\{{- \omega_{e}}L_{d}} & {{L_{q}s} + R}\end{bmatrix} - \begin{bmatrix}K_{Hdd} & K_{Hdq} \\K_{Hqd} & K_{Hqq}\end{bmatrix}} \right)^{- 1}} \\{= {\frac{1}{\Delta_{e}(s)}\begin{bmatrix}{{L_{q}s} + R - K_{Hqq}} & {{{- \omega_{e}}L_{q}} + K_{Hdq}} \\{{\omega_{e}L_{d}} + K_{Hqd}} & {{L_{d}s} + R - K_{Hdd}}\end{bmatrix}}}\end{matrix}$ $C = {\begin{bmatrix}{K_{Pdd} + \frac{K_{Idd}}{s}} & {K_{Pdq} + \frac{K_{Idq}}{s}} \\{K_{Pqd} + \frac{K_{Idq}}{s}} & {K_{Pqq} + \frac{K_{Iqq}}{s}}\end{bmatrix} = {\frac{1}{s}\begin{bmatrix}{{K_{Pdd}s} + K_{Idd}} & {{K_{Pdq}s} + K_{Idq}} \\{{K_{Pqd}s} + K_{Iqd}} & {{K_{Pqq}s} + K_{Iqq}}\end{bmatrix}}}$ $\mspace{79mu} \begin{matrix}{L = {PC}} \\{= {\frac{1}{s\; {\Delta_{e}(s)}}\begin{bmatrix}{{L_{q}s} + R - K_{Hqq}} & {{{- \omega_{e}}L_{q}} + K_{Hdq}} \\{{\omega_{e}L_{d}} + K_{Hqd}} & {{L_{d}s} + R - K_{Hdd}}\end{bmatrix}}} \\{\begin{bmatrix}{{K_{Pdd}s} + K_{Idd}} & {{K_{Pdq}s} + K_{Idq}} \\{{K_{Pqd}s} + K_{Iqd}} & {{K_{Pqq}s} + K_{Iqq}}\end{bmatrix}}\end{matrix}$

The PIDDC techniques described herein seek to utilize the forward pathcontroller C(s) 202 (see, e.g., FIG. 2A) to perform the decoupling,while constraining the feedback compensator H 206 to enhance the closedloop properties of the overall system. This implies that the twocross-diagonal gains of the feedback compensator H 206 are directly setas K_(Hdq)=0 and K_(Hqd)=0. The resulting open loop transfer function isexpressed as follows:

$\mspace{79mu} {L = {\frac{1}{s\; {\Delta_{eff}(s)}}\begin{bmatrix}{L_{dd}(s)} & {L_{dq}(s)} \\{L_{qd}(s)} & {L_{qq}(s)}\end{bmatrix}}}$     Δ_(e)(s) = (L_(d)s + R − K_(Hdd))(L_(q)s + R − K_(Hqq)) + ω_(e)²L_(d)L_(q)L_(dd)(s) = (L_(q)s + R − K_(Hqq))(K_(Pdd)s + K_(Idd)) + (−ω_(e)L_(q))(K_(Pqd)s + K_(Iqd))L_(dq)(s) = (L_(q)s + R − K_(Hqq))(K_(Pdq)s + K_(Idq)) + (−ω_(e)L_(q))(K_(Pqq)s + K_(Iqq))L_(qd)(s) = (ω_(e)L_(d))(K_(Pdd)s + K_(Idd)) + (L_(d)s + R − K_(Hdd))(K_(Pqd)s + K_(Iqd))L_(qq)(s) = (ω_(e)L_(d))(K_(Pdq)s + K_(Idq)) + (L_(d)s + R − K_(Hdd))(K_(Pqq)s + K_(Iqq))

As described herein, in order to obtain a first order closed loopresponse, the following is ensured:

L _(dd)(s)=ω_(d)Δ_(eff)(s)

L _(qq)(s)=ω_(q)Δ_(eff)(s)

L _(dq)(s)=L _(qd)(s)=0

By comparing terms on both sides, it is apparent that to performdecoupling of the flux terms, the proportional gains K_(Pdq), K_(Pqd)are set to zero. With this, the appropriate forward path controllerstructure is obtained as follows:

$C = \begin{bmatrix}{K_{Pdd} + \frac{K_{Idd}}{s}} & \frac{K_{Idq}}{s} \\\frac{K_{Iqd}}{s} & {K_{Pqq} + \frac{K_{Iqq}}{s}}\end{bmatrix}$

Accordingly, it can be appreciated that decoupling may be achieved usingthe forward path controller C(s) 202 alone without utilizing thefeedback compensator H 206. The latter may be used to enhance any closedloop properties of the system however. In other words, the decoupling isachieved in a forward manner without the need to perform state feedback.In situations where the feedback compensator H 206 is not utilized, theresulting configuration becomes a one degree of freedom (1-DOF) controlsystem. On further comparisons of the terms on both sides of the matrix,it can be seen that the cross-diagonal integral gains must be chosen asfollows to perform the decoupling:

K _(Idq)=ω_(q){tilde over (ω)}_(e) {tilde over (L)} _(q)

K _(Iqd)=−ω_(d){tilde over (ω)}_(e) {tilde over (L)} _(d)

With the cross-diagonal integral gains chosen as shown, the forward pathcontroller C(s) 202 is as follows:

$C = \begin{bmatrix}{K_{Pdd} + \frac{K_{Idd}}{s}} & {\omega_{q}{\overset{\sim}{\omega}}_{e}{\overset{\sim}{L}}_{q}} \\{{- \omega_{q}}{\overset{\sim}{\omega}}_{e}{\overset{\sim}{L}}_{d}} & {K_{Pqq} + \frac{K_{Iqq}}{s}}\end{bmatrix}$

In traditional approaches using a direct inversion decoupling controltechnique, the feedback matrix H is not utilized at all, and the directinversion decoupling control technique is therefore very sensitive todisturbance frequencies near the operating electrical speed of themachine and exhibits oscillatory behavior due to imperfect decoupling.Accordingly, the direct inversion decoupling control technique is notsuitable for many practical applications. Embodiments of the presentinvention address these problems by using the feedback compensator H 206to enhance plant dynamics, in conjunction with the forward pathdecoupling using the integral controller C_(I) 214, the resultantconfiguration performs better than prior decoupling controlconfigurations described in the art.

An improved inversion decoupling control (IIDC) technique is nowdescribed with reference to FIG. 5. This architecture provides adecoupled motor current control system with a first order response inboth the current loops. In particular, FIG. 5 depicts a block diagram ofimproved inversion decoupling control architecture 501 according to oneor more embodiments of the present invention. In this configuration, thefeedback compensator H 206 is used to introduce virtual resistances inthe system. In such cases, the diagonal elements of the feedbackcompensator H 206 are set as follows:

K _(Hdd) =−R _(d)

K _(Hqq) =−R _(q)

where R_(d) and R_(q) represent the virtual resistances in the d- andq-axis.

Thereafter, the decoupling and first order response characteristics areobtained by setting the control gains of the forward path controller C(s) 202 as follows:

K _(Pdd)=ω_(d) {tilde over (L)} _(d)

K _(Idd) =ωd({tilde over (R)}+R _(d))

K _(Pqq)=ω_(q) {tilde over (L)} _(q)

K _(Iqq)=ω_(q)({tilde over (R)}+R _(q))

The IIDC architecture 501 is much more robust to disturbances andimperfect decoupling in comparison to the direct inversion decouplingcontrol approach. In fact, the performance of the IIDC approach issuperior to the enhanced feedback decoupling control approach whenvirtual resistances are configured appropriately in terms of bothresponses to plant input disturbances as well as to imperfectdecoupling. This directly relates to the movement of poles and zeros ofvarious transfer matrices of the system with changing motor velocity.

Another improved inversion decoupling control technique is provided forsecond or higher order transfer function response. FIG. 6 depicts ablock diagram of an IIDC architecture 600 for second or higher ordertransfer function response according to one or more embodiments of thepresent invention. In order to obtain a higher order transfer functionin both loops, the forward path controller C(s) 202 needs to have adifferent structure, while the feedback compensator H remains the sameas in the case of the first order response. In general, to obtain an^(th) order transfer function, the forward path controller C(s) 202 isset as follows:

$C = \left\lbrack \begin{matrix}\frac{{K_{Pdd}s} + K_{Idd}}{{s\left( {s + \alpha_{d\; 2}} \right)}\mspace{14mu} \ldots \mspace{14mu} \left( {s + \alpha_{dn}} \right)} & \frac{K_{Idq}}{{s\left( {s + \alpha_{q\; 2}} \right)}\mspace{14mu} \ldots \mspace{14mu} \left( {s + \alpha_{qn}} \right)} \\\frac{K_{Iqd}}{{s\left( {s + \alpha_{d\; 2}} \right)}\mspace{14mu} \ldots \mspace{14mu} \left( {s + \alpha_{dn}} \right)} & \frac{{K_{Pqq}s} + K_{Iqq}}{{s\left( {s + \alpha_{q\; 2}} \right)}\mspace{14mu} \ldots \mspace{14mu} \left( {s + \alpha_{qn}} \right)}\end{matrix} \right.$

Accordingly, gains for the forward path controller C(s) 202 are selectedas follows:

K _(Pdd) =K _(d) {tilde over (L)} _(d)

K _(Pqq) =K _(q) {tilde over (L)} _(q)

K _(Idd) =K _(d)({tilde over (R)}+R _(d))

K _(Pqq) =K _(q)(R+R _(q))

K _(Idq) =K _(q){tilde over (ω)}_(e) {tilde over (L)} _(q)

K _(Iqd) =−K _(d){tilde over (ω)}_(e) {tilde over (L)} _(d)

Note that higher order refers to orders greater than or equal to secondorder.

When parameter estimation is ideal, the open loop transfer matrix forthe higher order response case becomes:

$L = \begin{bmatrix}\frac{K_{d}}{{s\left( {s + \alpha_{d\; 2}} \right)}\mspace{14mu} \ldots \mspace{14mu} \left( {s + \alpha_{dn}} \right)} & 0 \\0 & \frac{K_{q}}{{s\left( {s + \alpha_{q\; 2}} \right)}\mspace{14mu} \ldots \mspace{14mu} \left( {s + \alpha_{qn}} \right)}\end{bmatrix}$

and thus the closed loop transfer matrix becomes:

$T = \begin{bmatrix}\frac{K_{d}}{{{s\left( {s + \alpha_{d\; 2}} \right)}\mspace{14mu} \ldots \mspace{14mu} \left( {s + \alpha_{dn}} \right)} + K_{d}} & 0 \\0 & \frac{K_{q}}{{{s\left( {s + \alpha_{q\; 2}} \right)}\mspace{14mu} \ldots \mspace{14mu} \left( {s + \alpha_{qn}} \right)} + K_{q}}\end{bmatrix}$

It should be appreciated that, in general, a n^(th) order transferfunction can have n distinct pole locations, which may be achieved byselecting K_(d), α_(d2) . . . α_(dn), K_(q), α_(q2) . . . α_(qn)appropriately. A second order transfer function for either loop may beachieved by setting α_(d3) . . . α_(dn) and α_(q3) . . . α_(qn) to zero.In an example embodiment, n^(th) order responses in the closed looptransfer matrix with all closed-loop poles for each axis placed at thesame location may be achieved. If both loops are configured to have suchresponses, the closed loop transfer matrix is expressed as follows:

$T = \begin{bmatrix}\frac{\omega_{d}^{n}}{\left( {s + \omega_{d}} \right)^{n}} & 0 \\0 & \frac{\omega_{q}^{n}}{\left( {s + \omega_{q}} \right)^{n}}\end{bmatrix}$

In this case, the characteristic polynomials in the two expressions forT in both of the two loops can be compared to ideal second orderpolynomials. The comparison results in equations that can be solved toobtain the required K_(d), α_(d2) . . . α_(dn), K_(q), α_(q2) . . .α_(qn) in terms of ω_(d), ω_(q).

Another improved inversion decoupling control technique is provided fortransfer function response of different orders in both the q-axis loopand the d-axis loop. FIG. 10 depicts a block diagram of an IIDCarchitecture 1000 for transfer function response of different orders inboth the q-axis loop and the d-axis loop according to one or moreembodiments of the present invention.

The IIDC architecture 600 can be modified to achieve different closedloop transfer function orders in the two control loops (i.e., the q-axisloop and the d-axis loop). In general, in order to achieve n^(th) ordertransfer function in the d-axis loop and m^(th) order in the q-axisloop, the forward path controller structure may be expressed as follows:

$C = \left\lbrack \begin{matrix}\frac{{K_{Pdd}s} + K_{Idd}}{{s\left( {s + \alpha_{d\; 2}} \right)}\mspace{14mu} \ldots \mspace{14mu} \left( {s + \alpha_{dn}} \right)} & \frac{K_{Idq}}{{s\left( {s + \alpha_{q\; 2}} \right)}\mspace{14mu} \ldots \mspace{14mu} \left( {s + \alpha_{qm}} \right)} \\\frac{K_{Iqd}}{{s\left( {s + \alpha_{d\; 2}} \right)}\mspace{14mu} \ldots \mspace{14mu} \left( {s + \alpha_{dn}} \right)} & \frac{{K_{Pqq}s} + K_{Iqq}}{{s\left( {s + \alpha_{q\; 2}} \right)}\mspace{14mu} \ldots \mspace{14mu} \left( {s + \alpha_{qm}} \right)}\end{matrix} \right.$

Under the assumption of ideal parameter estimation, the open looptransfer matrix is expressed as follows:

$L = \begin{bmatrix}\frac{K_{d}}{{s\left( {s + \alpha_{d\; 2}} \right)}\mspace{14mu} \ldots \mspace{14mu} \left( {s + \alpha_{dn}} \right)} & 0 \\0 & \frac{K_{q}}{{s\left( {s + \alpha_{q\; 2}} \right)}\mspace{14mu} \ldots \mspace{14mu} \left( {s + \alpha_{qm}} \right)}\end{bmatrix}$

and therefore the closed loop transfer matrix is expressed as follows:

$T = \begin{bmatrix}\frac{K_{d}}{{{s\left( {s + \alpha_{d\; 2}} \right)}\mspace{14mu} \ldots \mspace{14mu} \left( {s + \alpha_{dn}} \right)} + K_{d}} & 0 \\0 & \frac{K_{q}}{{{s\left( {s + \alpha_{q\; 2}} \right)}\mspace{14mu} \ldots \mspace{14mu} \left( {s + \alpha_{qm}} \right)} + K_{q}}\end{bmatrix}$

The parameters K_(d), α_(d2) . . . α_(dn), K_(q), α_(q2) . . . α_(qm)may be selected appropriately to obtain the desired closed loop transferfunction orders with desired pole locations in both control loops(d-axis and q-axis) independently. As an example, in order to obtainfirst order and second order transfer functions in the d and q currentloops respectively, the forward path controller may be expressed asfollows:

$C = \begin{bmatrix}\frac{{K_{Pdd}s} + K_{Idd}}{s} & \frac{K_{Idq}}{s\left( {s + \alpha_{q\; 2}} \right)} \\\frac{K_{Iqd}}{s} & \frac{{K_{Pqq}s} + K_{Iqq}}{s\left( {s + \alpha_{q\; 2}} \right)}\end{bmatrix}$

Further, the forward path controller gains can be set as follows:

K _(Pdd) =K _(d) {tilde over (L)} _(d)

K _(Pqq) =K _(q) {tilde over (L)} _(q)

K _(Idd) =K _(d)({tilde over (R)}+R _(d))

K _(Pqq) =K _(q)(R+R _(q))

K _(Idq) =−K _(q){tilde over (ω)}_(e) {tilde over (L)} _(q)

K _(Iqd) =−K _(d){tilde over (ω)}_(e) {tilde over (L)} _(d)

The controller structure and gains described above are depicted in FIG.7. Under the assumption of perfect parameter estimation, the open looptransfer matrix for this case is expressed as follows:

$L = \begin{bmatrix}\frac{K_{d}}{s} & 0 \\0 & \frac{K_{q}}{s\left( {s + \alpha_{q\; 2}} \right)}\end{bmatrix}$

and the closed loop transfer matrix therefore is as follows:

$T = \begin{bmatrix}\frac{K_{d}}{s + K_{d}} & 0 \\0 & \frac{K_{q}}{s^{2} + \alpha_{q\; 2} + K_{q}}\end{bmatrix}$

In order to obtain a natural frequency ω_(q) and a damping ration ofξ_(q) in the q-axis closed loop, the characteristic polynomial iscompared to an ideal second order polynomial s²+2ξ_(q)ω_(q)s+ω_(q) ²which gives the desired values of K_(q) and α_(q2) as follows:

K _(q)=ω_(q) ²

α_(q2)=2ξ_(q)ω_(q)

In summary, the techniques presented here are significantly differentthan the prior art and are well suited for configuring a current controlsystem to be used as part of a torque control system for PMSM for EPSapplications.

While the present disclosure has been described in detail in connectionwith only a limited number of embodiments, it should be readilyunderstood that the present disclosure is not limited to such disclosedembodiments. Rather, the present disclosure can be modified toincorporate any number of variations, alterations, substitutions orequivalent arrangements not heretofore described, but which arecommensurate in scope with the present disclosure. Additionally, whilevarious embodiments of the present disclosure have been described, it isto be understood that aspects of the present disclosure may include onlysome of the described embodiments or combinations of the variousembodiments. Accordingly, the present disclosure is not to be seen aslimited by the foregoing description.

1. A motor control system that generates an output current from an inputvoltage comprising: a first module configured to: receive the outputcurrent from an electric motor as a feedback, the output currentincluding a direct axis (d-axis) component and a quadrature axis(q-axis) component; and generate a first voltage command based on avirtual resistance value, the feedback, and a targeted frequencycharacteristic of the motor control system; a second module configuredto: receive a difference between the feedback and a commanded current;and generate a second voltage command based on an estimated inductancevalue, an estimated resistance value of an electric motor, the virtualresistance value, a targeted frequency response characteristic of themotor control system, and the response of the d-axis component of theoutput current being decoupled from the response of the q-axiscomponent, the motor control system being a closed-loop system; and anaddition module configured to generate an input voltage command for theelectric motor by adding the first voltage command and the secondvoltage command.
 2. The system of claim 1, wherein the first module isfurther configured to compute the virtual resistance value based onoperating parameters of the electric motor.
 3. The system of claim 1,wherein the targeted frequency response characteristic of the systemimplies a change of the output current due to a change in the commandedcurrent.
 4. The system of claim 1, wherein the closed-loop systemincludes the electric motor, the first module, and the second module. 5.The system of claim 1, where the targeted frequency responsecharacteristic is a first order low pass filter with a tunable cutofffrequency.
 6. The system of claim 1, where the targeted frequencyresponse characteristic is a second order low pass filter with a tunablenatural frequency and a damping ratio.
 7. The system of claim 1, wherethe targeted frequency response characteristic is a transfer functionwith p zeros and q poles, p≤q.
 8. A steering system comprising: anelectric motor, the electric motor being a permanent magnet synchronousmotor; and a motor control system that generates an output current froman input voltage comprising: a first module configured to: receive theoutput current from the electric motor as a feedback, the output currentincluding a direct axis (d-axis) component and a quadrature axis(q-axis) component; generate a first voltage command based on a virtualresistance value, the feedback, and a targeted frequency characteristicof the motor control system; a second module configured to: receive adifference between the feedback and a commanded current; generate asecond voltage command based on an estimated inductance value, anestimated resistance value of the electric motor, the virtual resistancevalue, a targeted frequency response characteristic of the motor controlsystem, and the response of the d-axis component of the output currentbeing decoupled from the response of the q-axis component, the motorcontrol system being a closed-loop system; and an addition moduleconfigured to generate an input voltage command for the electric motorby adding the first voltage command and the second voltage command. 9.The system of claim 8, wherein the first module is further configured tocompute the virtual resistance value based on operating parameters ofthe electric motor.
 10. The system of claim 8, wherein the targetedfrequency response characteristic of the system implies the change ofthe output current due to a change in the commanded current.
 11. Thesystem of claim 8, wherein the closed-loop system includes the electricmotor, the first module, and the second module.
 12. The system of claim8, where the targeted frequency response characteristic is a first orderlow pass filter with a tunable cutoff frequency.
 13. The system of claim8, where the targeted frequency response characteristic is a secondorder low pass filter with a tunable natural frequency and a dampingratio.
 14. The system of claim 8, where the targeted frequency responsecharacteristic is a transfer function with p zeros and q poles, p≤q. 15.A method that generates an output current from an input voltagecomprising: receiving, by a first module, the output current from theelectric motor as a feedback, the output current including a direct axis(d-axis) component and a quadrature axis (q-axis) component; generating,by the first module, a first voltage command based on a virtualresistance value, the feedback, and a targeted frequency characteristicof a motor control system; receiving, by a second module, a differencebetween the feedback and a commanded current; generating, by the secondmodule, a second voltage command based on an estimated inductance value,an estimated resistance value of an electric motor, the virtualresistance value, a targeted frequency response characteristic of themotor control system, and the response of the d-axis component of theoutput current being decoupled from the response of the q-axiscomponent, the motor control system being a closed-loop system; andgenerating, by an addition module, an input voltage command for theelectric motor by adding the first voltage command and the secondvoltage command.
 16. The method of claim 15, wherein the first module isfurther configured to compute the virtual resistance value based onoperating parameters of the electric motor.
 17. The method of claim 15,wherein the targeted frequency response characteristic of the systemimplies the change of the output current due to a change in thecommanded current.
 18. The method of claim 15, wherein the closed-loopsystem includes the electric motor, the first module, and the secondmodule.
 19. The method of claim 15, where the targeted frequencyresponse characteristic is a first order low pass filter with a tunablecutoff frequency.
 20. The method of claim 15, where the targetedfrequency response characteristic is a second order low pass filter witha tunable natural frequency and a damping ratio.